Reduction of the three-dimensional Schrödinger equation for multilayered films

In this paper we present a method for reducing the three-dimensional Schrödinger equation to study confined metallic states, such as quantum well states, in a multilayer film geometry. While discussing some approximations that are employed when dealing with the three dimensionality of the problem, we derive a one-dimensional equation suitable for studying such states using an envelope function approach. Some applications to the Cu/Co multilayer system with regard to spin tunneling/rotations and angle-resolved photoemission experiments are discussed.